How does Medicaid work in Idaho?

No, your income does not come into it. I would call your Social Services and sit down with a caseworker. Sounds like Moms application maybe cut and dry.

https://healthandwelfare.idaho.gov/medicaid-program-income-limits

Be aware that there is a difference between Community Medicaid and Long Term Care Medicaid.

I assume that you have not been co-mingling your money with mom's money.

Your income does not count. She is applying as an individual.